3

Types of Modulation

·3.1. Definition
.. _. .

· Modulation is defifled as the p~ss by which some characteristics. us~ally amplitude. frequen;y or
phase, of a voltage (usually sinusoidal voltage) is varied in accordance.with the instantaneous value of some
other voltage. called the modulating vo.Itage. . ·• ·
. . ' - . .. ' .. .. . . . ' ,.• '

. The ~ -carrier is.applied to the voltage·whose characteristic is varied and the term modulating voltage
(or signal) is used for the.voltage in accordance with which the variation is made. · The carrier frequency is
the frequency of the carrier voltage being modulated. ·.. · . · · · . •· ·
. u·sqally the ~odulati~n freq~ency is considerably lower than the cmi~r frequency.' But thi~ is not
·• . inherent in the difinition and in exceptional cases, the carrier frequency may be lower ·than the modulation
· frequency as in carbon button transmitter or~ vacuum tube amplifier. ·
Let the carrier voltage be represented by the expression
fie =Ve COS (Cl>c' + 9)
where t = time •.•• (3.1)_

ro. e • =. angular frequency of the voltage ve in radians/second

.

and 8 = phase angle

... (3.2)
. ,
. where Jc is the frequency of the ·carrier voltage ii) Hz. • l
\ ·' .:J ' • :'

· ,The-inodul~tion process may then consist in varying one of the following three quantities : (,) amplitude
Ve '(ii) frequency roe and (iii) phase angle. 8 of the carrier voltage, in accordance with some function of the
. instantaneous value of the modulating voltage. · · , . . ,· , · ·. ·· · · · • . · . · ..,
Accordingly modulation process maybe classified as amplitude n:iodulation, frequency modulation or
ph~ modulation depending upon whether the amplitude Ve, frequency roe·or the phase angle 9 of the carrier
voltage is varied. Frequency modulation and phase modulation are sometimes grouped together under the
· heading angular modulation. It is possible to produce simultaneously, amplitude, frequency_and phase
}!todulation of the carrier voltage by varying all the three par~.'meters,. Ve, roe and 9 simultaneously but in
commercial·radio transmitters, care is taken to produce only one type of modulation with the excfusiortof the
other two. · · ·
. . ''. .
_3.2. Expression for Amplitude Modulated Voltage
In amplitude modulation. the ampUtude of the carrier voltage varies in llCCOrdance with the instantaneous
value of the modulating voltage. Let ~e modulating voltage or the signal be.given by the expression, ,. .· ·
. . , . . ~ \ . . . . .· . ~ .

,... v,,, ._=V,,;cosro.,.t . ·- . -· .•.- ·... (13)

· where c.o,,, is the angular frequency of the signal and VIII is ~ -amplitude.
 RADIO ENGINEERING
30

Let the carri er voltage be give n by the expr essio n,

= Ve COS W,J .. . (3.4)
tic

phas e angl e 8 has been take n~ zero . sinc e it

does not
In Eq. (3.4), for conv enie nce in calcu lalio n, the ralit y of the
how ever , does not in any way rt!duce the gene
play any _part in the mod ulati on proc ess. This
expr essio n .. time as
er no long er.re main s cons tant but varie s with
On amp litud e modulal.ion, amp litud e of the carri
give n by the folJowing expr ession : I
V (t)= Ve +K,. . V,,. co~ ro,,. t ... .(3.5)
I amp litud e.
J where A;"., . V,,, cos co,,, t is the chan ge in carri er
ge is the n give n by ,
The insta ntan eous valu e of mod ulate d carri er volta
V = V(t) COS COc I · . .. (3.6)

or V = [Ve+ K., V,,. COS W,.. l] COS We I . .. (3.7)

..Eq . (3.7) may be written as,

K. V,., ]
v = V [ 1 + -v,- cos co'" t cos w
C
C
I

v = VC [ I + m • cos wm t] cos wC t . .. (3 .8)

fa ctor or dept h of mod ulati on· and is give n

by,
where m., is the mod ulati on inde x or mod ulation
K . V,..
m == -- ... (3.9)
- V,

· 100 x m., gives the percentage modulation .

3.3. Wav efor m of Amp litud e ·M odul ated Volt age
s th , f
Fig. 3.1 (a) show s the wave form of unm odul ated carri er volta g·e · Fi·g · 3 •1 (b) g·ve
· 1 e wav tl0rm o
.
· ·da1 d l · • efqn n of amp litud e mod ulate d carrier volta ge.
smuso1 mo_ u atmg voltage. Fig. 3.1 (c) give s the wav d
· ·
From Fig .. 3.1, we. see that frequ ency of carri er rema ins unal tered but 1·rs amp litud e vane s m acco ·
r ance
. ·
. the vana . of the. mod ulatm
. uon . g voltage v,,,. ·
with
It niay furth er be seen that,
V
m =Ve,_.Ve. - C
... (3.10 )
a

Also · : .. (3.11y .

Hen ce . . . (3.1 2)
. the
· With the heJp of Eq. (3 .12), the mo~ ulati on
mo may be expe riine n~ll y dete rmin ed by appl ying
ying a suita ble
n plate s of a cath ode ~Y osci llosc ope and appl
amp litud e mod ulate d volta ge to Y-Y d~fl ecuo Fig. 3.1 (c)-t hen appc.ars
~fle ctio n plate s. The patte rn show n in
•swe ep volta ge (tim e-ba se volta ge) to theX -X ulati inde x ma}'
on
of_Ve ....z and Ve,,.;,; may be obse rved . The mod
on the screen of the CRO from which valu es
then be calc ulate d.
TYPES OF MODULATION • 31 ·

-u

~t
-U
>u
" 0 (a) . Unmodulated carrier voltage
::.u
~

it
>E
,, 0
~E I Timc,t (b) Modulating voltage
I
-L-~--
1

-
3
WI
Envel-ope ~avm coswmt
0
u
,........
... Vcmox
!
Ill
0 14+1...+H~ ~H-~M+l-l-H-++
_L
t-+t+f +H-ifH++-11 H-H+tlftttt.-\c
...;=
Ve
rmj_ -
1 (c) Amplitude modulated voltage
0
u
.. I Ir - Timc,t-
..
E
...:::.,
~
I
!)

Fig. 3.1. Waveform of amplitude modulated carrier voltage.

3.4. Sidebands Produced in Amplitude Modulation .
Eq. (3.8) for amplitude modulated carrier may be expanded in the following form :
. ma Ve ]
fl = V cos w t ;.. - - [2cos we t cos ro,,. t
C C 2

, m m
or f/ = V cos ro t +-g V cos (w + ro ) l +-;,: V, cos (we -- W,..) l .. . (3.1 3)
'' 2' '"' .!,,

Eq. (3.13) reveals that the sinusoidal carrier voltage on being amplitude modulated by a single sinusoidal
modulating voltage consists of the following frequency tenns : . ·.
(t) Original carrier voltage V, cos we t of angular frequency Cl:)c.
(ii) Upper sideband term"'; Ve cos (w, + w,,.) t of angular frequency (we + w,J .
.
Ill

(iii) Lower sideband term ; Ve cos (w, - ro,,.) t of angular frequency (ro, - ro,,.~.

The lo;,..,er sideband term and the uppe~ sideband "terms are located in frequency s~ctrurµ on either side
of the carrier at a frequency interval of w.,. as shown in Fig. 3.2. TI1e magnitude of both the upper and lower
sidebands ism,. 12 times the carrier amplitude V,. If modulation index m. is equal to unity, then ~ch sideband
has amplitude.half of the carrier amplitude. ·.
. Fig. 3.2. shows a _wot of the frequency spectrum of the amplitude m~ulated voltage. .
· ·· Amplitude inod~lation thus shifts the intelligen~e from audio frequency le.vel to the level.of carrier
frequency roe. Also the intelligence appears in the form of two sidebands symmetrically placed relative to the
; ' . ..
 • RADIO-ENGINEER

carrier frequenc y Cl>c.. Each of these sid

carries the complete intelligen ce ori ·
containe d in the signal before modulati on.
· . • intellige nce occurs twice in an ampli
• modulate d carrier. ·

· Eq. (3.13) ·· reveals that ampli the

· Carrier . modulate d carrier .voltage consists of
t
T ..
sinusoid al voltages
"' .·
of · amplitudes.
.

Ve• ; Vcand .; ~"' _respective ly and an,8 _ __

Lower
sideband •
Ve Upper- ' .
Q. sideband frequenc y _co.;·, (roe+ w..) and(roc - ro.. ) respec.
E
<( mav. lively. These may, therefore , be represen~
2 C
by the sirior representation of Fig. 3.3 which
0 lwc-wrrJ We (we+ W,:nl "'
. shows two sideband s of amplitud e ; Ve each
Angular freQuency...;....
, .
rotating with angular velocity ro.. with respect
Fig. 3.2. Plot of frequenc y spectrum of amplitud e modulate d to the carrier of angular frequenc y·
roe. The ·
voltage. resultant of these three sinors givet lhe
amplitud eoftheres ulcantam plitudem oduJated
voltage.

., .

' .
lower ·Upper
Modulo-t ing sideb
· signal g Cw) sideband

Ve

0 w, ,•~z) •'
(Wc-
(w.;-w1) I We•~tJ '
frequcnc y _ . · ·

Fig. 3.3: Sinor repre;en tation of amplitude . · · Fig: ·3 .4. Frequen cy spectrum of a complex modulating .
modulati ng voltage. . · ypltage and amplitud e modulate d voltage.

. "s orai we hav~ assumed ·the ~odulati ng signal to be.a single frequenc y tone.. In pracri~~ however , the
ed by
modulati ng voltage has a complex waveform . If the modulati ng volt;tge is periodic, it may be represent
ted by Fourier
· Fourier series. On the other hand, if the modu.Jating voltage is non-peri odic, it may be represen
~s and
integral. In any c~. the modulati ng signal consists of a band of frequenc ies of different amplitud
modulati ng signal produces on modulati on,
phases as shown in Fig. 3.4 by g(c.o). Each frequenc y term in this
s symmetr ically disposed
a pair of sideband terms. The entire modulati ng signal then produces two sideband
about the carrier as shown in Fig. _3 .4. Here Cl>i and 'Wz are the lowest and the highest fr~uenci
es in the ·
modulati ng signal.
·3.5_ -Power Relations in Amplitu de Modulated Wave .
·We have seen Li,at the carrier compone nt of the. amplitud e modulate d wave has the same amplitud e as
two sideband compone nts as well.
·, the unmodul ated carrier. However , the amplitud e modulate d wave contains
·Further,
Evidentl y,·therefore, the modulate d wave contains more power than. the carrier before modulati on.
powe,- in the modulate d .
~ .since·the, amplillld e of the sideband s depends on the modulati on index, the total
 33
··TYPES OF MODULATION
essed
The total po~er in the modulated wave may be expr
wave wi!i also depe~ds on the modu_lation in~ex. ~ • • •

• • • - • •
. : •

as, ~• • .. • •
.. • • .
I . . • I

· ...(3.14)
•• I :•

2 2 .
I v_
2
Vua Vus,
-+-+- I ,:,(3,15)
p =-R
- or
... .
• I .R
R is resistance in which the power is dissipated.
R .

where all the three ·voltages are r.m.s. values and

odulated carrier po~er and is given by,
The first term on th~ RHS in Eq. {3.14) is the unm .; 2 .

V!" =(V/{-i)=VJ
- . ...(3.16)
p = - - R '2R
.c . R · ,

., .. r
Similarly, ' • ' • I

-~(m·:rJ x¾=m;::= ::-i . ·... (3.17)

Substituting Eqs. (3.16) and (3.13) into Eg. (3.14): we get

I

.. ·· -- .
. .. (3.18)

' ... (3.19) .

or
e modulated wave to the_unmodulated carrier power
Eq. (3.19) r~lates the total power P, ill the amplitud ~
. .

.
~e AM wave is P,_=·1.5 ~c when m =
.
L, .
Eq. (3.19) _reveals that the maximum power in
measure the modulated and unmodulated carrier
Calculation or Curren(. 'often it is relatively easy to pute • ·
nts. Such a situation arises when the ~nte nna current of a transmitter is metered. ·We may then com
curre '· · " · · · · , ··
', · ·
the modulation jndex m,, from these two currents. --.
Lell e be the unmodulated current and Jet/, be the
total or the modulated current of an AM transmitter,
currents being RMS values. LetR be the resistance into which these currents flow. . .. . •
both
·: P, I I, R
- =- =
I,
- = 1+
mo
-2 2 ( ')2 • l
Then, . · P . 12 R IC . . . ·
C C • • '1

.Hence
• II
-=
1,
• m22
· M+- } • " . .-.(3.20)
t :J 't.

or • I, = le -\/ 1-+;f2
- r;; · ... (3.21).

carrier is m~ late d by ·se~~~al sine wave~ simul-

• Modul~tion by Several Sine Waves~ In practice, ng
power condition. The proce~ure consists_in calculati·
taneously. It"is ~f in~erest to calculate th~ r~ult~n~ Eq. (3. J9) to compute the·total power P,.
the total modulatmn mde. x and then substitutmg 1t m . .
. : .' ~7 .
 34 ••••
_There~ two methods of computing the total modulati~n in~ex m,. These are give~ below. .
. Method I. Let V., V2 , V3,-etc. be the simulraneous modW:3~g. voltages. Then the local modu
.-voltage V, equals the squart; root of the sum of the squares of the mdiv1dual stages.
. -----~-=-- ..
Thus

On dividing both sides by Ve, we get ··- .

., .
V, vt+ v;+ v;+ ...
-= - - -v- -
· -=
Ve - C

Hence ... (3.

Method II. Eq. (3.19) may be written as,
. . m,,1
P, =Pc +Pc T=Pc + PSJJ . ,·.(3.23)

where P 58 is the total sideband_power and is given by,

... (3.24}

When several sine wa ves simultaneo usly modulate the carrier, the carrier power Pc remains unaltered
but the total side~and power PssT i~·now the ~um of the indjvidual sideband powers~- Thus, ~e get ·.
. .. (3.25)
-(?ri substituting ~q. (3.24) i1!tO Eq. (3.25), we get
fl
1
Pcm, Pcm? Pcm; Pcm;
~ =-2-+ - 2- + - 2-- + ...

Hence . 2 2 2 l
m, = m 1 + "'-i + ~ + ... . .. (3.26}

It may be noted that this total m~dulation index m, must not exceed unity or else distortio~ will result.
·· · ·. · Example 3.1. A sinusoidal carrier voltage .offrequency J NfHz and amplitude JOO.volts is modulated
by a sinusoidal voltage offrequency 5 kHz producing 50% modula_tion. Calculate the frequency and amplitude
of upper and low_er sidebands. · ·
Solution. Frequency o_f u~per sideb~d
= 1 MHz+ 5 kHz= 1005 kHz.
Frequency of low·e r sideband

• '.
= l MHz - 5 kHz ·= 995 kHz.
Amplitude of each sideband tei·m

m,. 0.5 · ·. · . ·
Ve = x lOO=volts. Ans.
2 2
, . Example 3.2. °The tuned circuit of the·oscillato~ in asimple AM trans",itter uses a coil of 40 µII and
hunt capacittJr of value 1 nF. If the oscillator output is 'modulated by audio frequencies upto 5 kHz, what is
he.frequency range occupied by the sidebands? . ·· ·. · · ' ' .
' \
 TYPES OF MODULATION 35 .

Solution.
1 . . 1 . ·
le ""- ~=-r ==== ==~= =H = 7.96 x 105 Hz
.
LWVLt.. . ·
'2Jt'V40 X 10-6 X 1 X lo-'
=796kH z.

. , · Since the highes! modulating ~requencY. is 5 kHz, the frequency-range.will extend fro_ m 5 kHz below
791 801 kHz. . . •. . .. , . . ·. _.. .
to· S_~ above the earner' frequency, (.e. from to , . . ~

a sinusoidal
Examp le 3.J. A sinusoi dal carriervoltag~ ofamplitude J00 v~lts is amplitude modula ted by
amplitude of 120 volts.. Comput e the
voltage off~eq14ency 10 kHz resulting in maximu m modula ted carrier
· ·
modulation inde~.
.. - · · · "V~ .:. V - 120- 100 . ·
Solution. :: m. = -;, . =0.2. Am.
100 .
. .. .
ted bya sinusoidal
.· . Examp le 3.4.A sinusoi dal carrier ~oltage offrequen cy 1200 lcHz is amplitude modula
carrier amplitu des of 110 volts
voltage off~equ ency 20 kHz resulting in maximu m and minimum modulated
lated
and 90 volts· respect ively. Calculate (a) the frequen cy of lower and upper sidebands (b) the unmodu
carr_ier _ampUtude (c) modula tion index_and amplitude of-each sidband.
Solution·~-
. __(a) Lower -sideban d frequen cy =(1200 ~ 20) kHz= 1180 ~ -
Upper sideban d frequen cr . = (1200 + _2q) kHz= 1220-kliz..
Ve~+ Vcnu: -. .: ·
(b) Unmod ulated carnier amplitu de Ve= 2

= (llO + 90) = 100 volts.

• • ._t.
2 '- . . ··.. . . . '

m
(c) Moulati on index · •

(d) ,\mp!iwde of each side~ d

• ', •

• :: ' . '
•

,' ,-:. _·::

•

>;,~~ ~~ • ·/ , I

= 0.0~ ,>< I 00 = 5 ~Its. A..._

·
and (b)
~i
Example 3$. Therms value a·c~rrier voitdg~ is _JOO v~lis. Co-;;,pute its~ ~alu_e ~hen
40%.
it has beert
.
amplitu de modula ted by a sinusoidal audio voltage to a depth of (a) 20%
Solution. . •. . .. . \ J
•~ P t _+ m:] ,·• · : : • .

~ · 1· • • ' . . • ·. , .· • :1, i, , ·: . ·, ,. : '· \ .9. 2 .. .,.. .. .•.· . .· .\ (. i· ;'r . •. •

or
y2,_
T -~~
y2"" [
_1 +2
m.2]
..
. Hence
. .

.
. or . V,., =V':'" , :
. . .• 1. •

•
. :36 . RADIO ENGINEe

(a) ~•- = 100

. ✓
°1
(02)2
+T= 101 volts ..
.•

(b)
.. V~ = 100
.
✓
---- .
(04)
I+-·2 --
2
= 103.9 volts.
.
.

. . . .
· Exam pie 3.6. Therms value of a radio frequency voltage is 80 volts. After amplitude moaulatio,i bJ
sinusoidal audio voltage, therms value of the RF voltage becomes 88 volts. Comp~te the modulation i

Solution.
.
(,nu = vcarr [1 + 2
ma 2]
·,
Hence ·

Examp!e 3.7. Unmodulated RF carrier power of 10 kW sends ·a current of 10 a,,:ip rms through an
antenna: On amplitude modulation by another sinusoidal voltage. the antenna cu.rreni i'ncreases to 11.6 a,,p.
ca/cu/ate (a) the modulation index and (b) carrier power after modulation.
~ ... • t
· • (' . ,

Solution. Let rm" antenna curre nt before and after moduiation be / and I rcspectivel-)'.. 0

Then

Power of carrier after modulation .is given by,

♦

• • - • I

Example 3.8. Therms value of a carrier voltage after amplitude modulation to a depth of 40%' by o
, sinusoidal modulating voltage is55 volts. Calculate therms value ofcarriervoltage when amplitude modulated
to a depth of 80%. · ·
.' V,~ 55
Solution. V =--;:::==== -==== 52.93 volts.
carr : ✓ l + (m; /2) ✓ 1 + (0.4) ,/2 2

. ·. .
'' ..
.At 80% modulation, the modu'Jated carrier rms voltage is given by,
• r-

' v~ = V~~ \F~= 5~.93 ✓ 1'+ <~:)' = 60.81 . ~o,:s.

' - -
Exampl~3.9.-A J kW carrierismodula;~d toadepthof60%. Calculate the total power in the modulated
wi;ive.

· Solution.
,
, .P, =::- Pc [1 +-
m!] =· 1' [1 +(0.6)
- -.
2
]
= 1.18 ·
kW. .
. 2. . . 2. . . .
. , -
Example 3.10. A broadcast radio ,r;ns",r,itte~ radiates 8 kW when the modulation percentage i~ 50.
What is the unmodulated carrier power ? ·
P, . 8 ·.
Solution. Pc = 2
= - - -2 - = 7.111 kW.
1 + m., / 2 1 + (0.5) / 2·

•
_ TYPES OF MODULATION 37

- Example J.it. A br~adcast tr~_nsmi1ter radiates 4.72 kW when the. modulation perr~ntage is 60.
Calculate the total power wh~ the modulation has been reduced to 40. per cent. -
" ; '

· Solution. p -~ P, = · 4.72kW ~ 4 kW
c 1+ m; I 2 • 1 + (0.~) 2 / 2 ·

With 40 per cent mod~lation,' ·

I• f

. P, = 4kW[t + (0.~)2] =4-[1 + ~.08} =4.32 kW: ..

' . 2 .
. Example 3.12. A radio telephone transmitter using amplitude modulation has unmodulated carriu,
output power of20 kW.and can ,be modulated to a maximum depth of8()/fr; by a sinusoidal modulating voltage
without causing overloading. ·Find the value to which unmodulated carrier pow.~, may be increased, without
resulting in overloading if_the maximum permitted modulation index is rest~icted to 60~. ·
Solution•. Modulated carrier power
2
." m.2J =·
P, =Pc (1 +2 [ (0.8) ] ' •
20 1 +-_-2- ·= 26.4 _
) . . .
This is.the maxirQum power which can be handled by the transmittgr witho~l-causing ov~rloadir.g. The
increased unmodulated C8:fTier power is then.given by, · ,• :; •

26:4 =Po'[1 + (0 6)2] = .1;18 P/

2
Hence . . P ' = 26 .4 = 22·.38 'j(W•
0 1.18

Example 3.13. A ,a.dio tr~rismi~ter radiates JO kW wilh the c~rrier unmodulated and l 1.25 kW when
the carrier is modulated by a sinusoidal voltage. Calculate the mo_dulation index. Anqther sine wave is capable
of producing 30% modulation. If both the sine waves simultaneously modulate the carrier, determine the .
total radiated power. ·
2 p • 11 25 ' I
m, =_!, - · 1 = _ . _:__· 1 = 0.125
Solutl~n. 2 P0 10

_' Hence 1· mv = ✓2 x0.125 = 0.5

.. "\ . ) : ,,' ..
:
. • .I . . I ' .'
With simultaneous modulation by the two sine waves, ~ . ...
-~-- .
~
'
-: .:·._ m~=-✓m; +m;: ✓(0.5) 2 + (0.3i = 0.58
- .. .. 4 I I '
2
• •
··
~

Hen9c P, • P, (1 +~) = 10[ l +(~.SB)']= 1{.7.kW.

. .
3,6, Deffnltlon or Frequency Modulation _
; .

Frequency modulaticn consists in varying the frequency of the carrier \'.Oltag~ in acco~dance.~ilh the
~nsranraneous value of the modulating.'t'.Oltage. • . ·· -.: , • ·, · ;.. ; ·. _
• · Thus the amplitude of the carrier does not <:hange due to frequency modulation: This is an advantage
since any incidental disturbance such as aunosphcric disturbance or Jll&n made _static primarily appears. in the
form of variations ofamplitude orthe carrl~r voltage and may be eliminated in a frequency modulation receiver
which is made insensitJvc to amplitude variatibn.

•
 RADIO ENGINEERING
38
- · .- . · ·.
I 3.7. Waveform of Frequency Modulated Voltage -
have amplitude vc and frequency ooc radians/sec and let it be given by, ·
I
I
I ., ' - · • · 1 .
! . _ Let the earner vo r.age v,
v = V sin oo. t
•.. (3.27)
C & , ..

·er vo'tage r1.,.. For ~imp!icity tho modulating voltage is also assume.d to be.
. _ .
Fig. 3.5 (a) shows th e carrl ,_ ~

· · · ' ·
sinusoidal and let it be giv1Jn by,
...(3.28)
i,111 = VIll cos 00,,. '
i·
I

..
- -,rI ,-· - -·1vc
I ~
il~ I ~
I.
Tim e,t..... (a)
~1 I -I ~

I r
f I .I
C: E
.. I I I
·2 g3 - - ,- - - ' - - I -- -
I Vm (b)
oo --~.. .L.
~-oo ~--
III
--'l<- ---,- ---#- ----'-
i5o u .t I Timr. t-
0
:1
>
>E _ __: j ___- _.__
._ I I· I •

I I . I ·,
- ·I · ·I
l_
11 J ~, ·- ... - 7 - - - - ,._
I
a~~o~ ;+++ .~~~~ 4+~-1 +1-~+ U~u.u .~~- -
. ";.!! S' I/ ·~I /I · Time t -
, ~ t!: · I t J
l: 8 ~ .. Ii. -- l ~- - ·- I .ii
I
·I
! I
I
I (c) Modulated carrier voltage.
I . .I I . I I· . .~. '

I I I 1· I
~ I .. . J
I. .
I
I
-I
1
I
I
I ~ f
I . I
'. I
I
I
I
I
I

I
, .I I

. (o) Instantaneous carrier frequency versus time curve_ . . .

Fig. 3.5. Waveform of frequency modulated ~arrler. voltage. · · • :: ,
.
fig. 3.S (b) shows the modulating voltage 0111 • Fig. 3.5 (c) shows the resulting frequency
modulated
It may be seen
carrier voltage. Fig. 3.S (d) shows the variati~n of instantaneous carrier frequ_ency with time. ting voltage.
that this frequency variation is identical in form with the variation with time of the modula
neous value of
;vidently the frequency variation called the frequency deviation is proportional 10 the instanta
'
.,·
·~
•
 TYPES OF MODULATI.ON 39
~

.the mod~lating voltage. The rate _at which this frequency variation rakes place is obvicni~ly equal to th~
modulatmg frequency. In FM, all signals having the same amplitude will deviate the carrier frr.quencyby the
same amount say 50 kHz, no matter what their frequencies. Similarly aiUhe modulating signals ot the same
frequency, say 1 kHz, will deviate µie canier at the same rate of 1000 times per ser.ond, no matter what their
individual amplitudes. The amplitude of the frequency modulated carrier ~~mains consWit at all times during
frequency modulation. . . . : · . _• . . , . . _ . .
3.8.· Mathematical Expression for Freq~ency Modulated Voltage •
. Let the sinusoidal modulating voltage be given·by·the expression,
fl,,. =V cos ro,,.
III 1 ... (3.29)

where ro~ is the angular frequency of the modulating v~ltage in rad/s~ ~d Vm

.. is its am.pliwde in volts.
Let the carrier-voltage be given by,
· fl, = v, sin (ro, 1 + 8) ... (3.30)

where ro, is the angular frequency of th~ ccirrler in radisec. · '. -· ,

Ve is the amplitude of µie· carrier in volts·and e_c is the phase a_ng!e in radians. ·_. :·: · : ·
'• .
- Let 4> = ro, t + a ~ , .. (3.31) .
I .

: in Eq. (3.31), 4> is the toiat in~tantaneou~ pha:s~ nngle of tl1e.c31!icr volia"ge so that Eq: (3.30) may be
. - . . . . . . -
put as, . .
fie = V, sin 4> .
.. ;{3.32) • • • • ': . ~ ..... J,

- : Obviously ~he angular·frequency roe is r.elated to the phase angle ~ by ~e relation,

. ' : .

Cl)
d~ .
=- ~ ·.. .) ' .. . .. ' ... (3.33)
. ' dt . . ...
.. . . . . . ." ~ (

On frequenc modulation, the frequency of the ~artier no longer remains CO?Stant bu~ varies_ with .time .
• accord
m ance w1·.th thyein"tantaneousvalueofthe
::; .
modulatingvoltag~.
. _
Thus the·frequency _o..fthecamervoltage
. , .
after frequency modulation is giyen by. . . . .. • ·
:ro =.roe +_k1 : fl,,. ... (3.34)
, .
· ·_.. . . = ro~·+ k1 : VIII cos ci>,,, t _ . ... (3.35)

where", is the constant of proJX)rtionality. . · · . . _· ~ · . · ' . •

. · · Integration of Eq. (3.35) yields the phase an~le _of the _modulated cam_er voltage. Thus,.we get
~ =fro d1.= J[ro~ +ic, v,,. ~os ro,,, ,1 d, . . .. (3.36>

1 '
or ""
'I'
~ roc , , +k'I v"' -Cl) sin ro,,. , + 81 . ,',.(3.37)
, Ill ,;
. . ~

.. where e, is the constant of integration and represents a constant phase angle.

Angle 91 ~Y be n~gl~ted in the following analysis since.it is insignificant in the modulati~n p;ocess.
ijence the frequency modulated carrier voltag~ is given by, · · ··

• ~ V, sin [ Cll, r +k,':: sin ro. ,] ... (3.38)

. \
40
- ...
From.,Eq. q.3,5) insrantaneous freque~cy of frequency·n;odulated carrier voltage
in Hz is giveo
(i) .. . v,,.
J =-=
.2 7t
fc +. 1c1' -2 1C cos
. .
ro,,. t
, .'
· The maximum value of frequency~ given by,
. v,,.
•
. . =,J c +k1 . -27t.
I.~
The i:ninimum value of frequency fa ·given by,

) .

Thus the freque ncy deviation, i.e. the maximum variation in freque
.
ncy from
' ..
the _mean value ,is
-,
.
.,

b¼,
v'"
/, = /,,.n ~le= fc - /,,.;n = k, 21t
cy and is also indica·
Modulation index m1 is the ratio of frequency deviation to modulation f~uen
by 6.
. ,;,(3.43)
Thus

Thus the expression for the frequency modulated voltage is given by,
... (3.44)
fl = Ve sin (CO~ I -1: m1 sin CO"' t)

ating volt.lge amplitude

-It may be noted that as the modulating frequency w,,.·decre.ases and the modul
forms the basis for distin•
remains constant, i.e. ro, remains constant, the' modulation inc1ex increases,. This
guishing frequency modu_lation from phase modulation .
. . Example 3.14. In an FM system, the frequency deviation is5 kHz wh,;n ihe audio
modu/ari11gireq~nc1
Also compute the/req~ncy
is400 Hz and the audio modulating voltage is 2 V. Compute the modulation index.
deviatio,rand the modulation index J/(i)AF voltage is increased to 6 Vkeeping modul arionfr~quency unaltered
{ii) AF voltage is increased to 8 V while the modulation frequency is reduce
d to 200 Hz.
Solution.· With "AF frequency 400 Hz a~d·AF ~~ltage 2 V, f:t = S kHz
Hence modulation index

. Further/, cic V,,..

I, S kHz · ~ · ,
-V • - = 2.5 kH?/volt (of modulating voltage) •
Hence 2 VO1t . .
/ Ill

Case I V,,. a 6V

• Hence _/, s 2.5 x 6 a 15 kHz

· /, 15 kHz 11.
Hence m, •7:.• 400Hz • 37'"
TYPES OF MODULATION 41

~ase n. : V,,, =8 V ; /,,, =200 Hz

Hence /, = 2.5 x 8 = 20 kHz
•
h 20 kHz
Hence m1 - - - - - 100.
- /,,, - 200 Hz =
~

by the voltage equatiQn : .

. Example 3.15. An FM wave is represented .

v= 20s in( 5xl 0 t+4 sin1 500 t) ·. · · .·

6

.
i~r a,:,_d modulating frequencies, the mod ulation index and the maximum deviation of the FM
Find the'carr . · .
a 20 <Jhm resistor _? -
. What power wzll this FM voltage dissipate in _
Solution. FM voltage is given by, .'
. .
- s·x 108 . . 7
- - Hz=7.96 x 10 Hz
/. =27t
Obviously then · C

1500 ~
f. = - Hz= 238.7 Hz
"' 2_7t

m1 =4.
Modulation index
Frequency deviation
/ 11 = "!, •f,,, =4 X 238.7 ~:. =955 Hz
. ' ,

- V,;.,·__,.;._
(201..__ tt .
{'2)2__- - 400 - 1· 0·was
P __ R 20 2x2 0 ·

3.9. Frequency Spectrum or the FM Wave

amp litud e m
· odulation, only two sideband term s are produced namely the upper sideband term and
. In y modulated
the lower sideband term. Situation is more com
plex in F.M. When a carrier voltage fie is frequenc
ier voltage is given by. Eq. (3.44) reprodu ced here : . .
sfnu soid al voltage fl,,., the mod ulated carr . .
by a single .
... (3.45)
ri = V, sin (w, t + 5 sin 00111 t)
the solution involves-the use of Bessel function,·
s. On
'fhis equation involves sine of a sine. Hence 5) _ ;
(3.4 may be expanded to yield,·
using Bessel functions, it may be shown that Eq.
fl== v, '+
[Jo (5) sin ro, J, (6) {sin (ro, + ro,,,)' - sin (w, -
(1)111) t)]

+la (I>) (sin (w,·+ 2 w,,.) I+ sin (ro, - 2 ro,,.) t} . •

•
+ J, (a) (sin (W, + 3 ro,,,) I - sin (W, - 3 ro,..) t}

+J4 (l>) (sin ((.I), +4 w,,,) I +sin (ro, - _4 (.1) t)

111
)

+ ......etc, ... (3.46)

.
ilinusoidal
ier voltago after frequency modulation by another_
.
Eq. (3.4~) reveals thut the sinusoidaly carr · ·
vol ~c consists of the following frequenc termt,
(6). .
~ .~ie r voltag9 reduced in magnitude by the fac~r / 0
r;.J:•t
.. ~-
 42
RADIO ENGINEE~
(ii) infinit e numbe r of sidebaml terms on both lower and upper freque ncy sides
<;f the c.arri
qucnc y at intervals equal to the modulation fr~ucn cy. _The amplit udes of these
side~a nd terms ~e vc mut:r
by various Bessel functions of the first and ~1.fferent orde~s denote d by the subscn
plS. · p
Bessel function J,.(6) is given by,

,'. (~) = Wl\- 1.i'~::):) , i~:2;) , :);t, ~ ----J +2

. .
+ 3 /~: -.--(3.
In order to find the amplit ude of a given pair of sideba nd terms and the magni
tude of the carrier it
necess ary to know th~ value of the corresponding Bessel function. It is, however, not necess ary to
evai
the Bessel function using Eq. (3.4 7) since the magnitude of Bessel functio
ns of this type are readily avai)ab
in table form as in table 3.1 or in graphical form as in Fig 3.6.

1·0

·- 0•8

0•6
~ ~rfl.'.,,(b
'·
t. 0·4 K r>: ~ ........
I )< / '\ \'
'I"
J,,_(~) .
/' ~ (&"

JnC&) 0-2

-,n
0

-'1-~
I~ V_.
I
,/
\

• \ J

\I\,._
' \
'
-> '
/ '-- K.- ,,,.. - -
- )><, - ~,....
/ -"> ~ "-- r---..
I/ y
,: "\SlX/ ') V' ~ 'f"). 0U /
'-
lJ

- --~ S-
./
..--
V '\
,I
/ ' '\
/I ' • l !J
~

- 0•6

_
F ig. 3.6. Bssse! function of the first kind and different order.
_.. The follow ing conclu sions ~e drawn from the forego ing study and fr.o m Table
3.1 and Fig. 3.6.
(z) In AM only three frequencies namely the carrier and the two sideba nds are involv
ed. FM, on
the other hand, has carrie r and an infinite number of sideband terms re<;urri
. .
ng at freque ncy interva l of/,,,.
. Table 3.1. Besse l Functi ons of the Flr~t Kind

X
nor Order
(m,) Jo J, ./2 J3 J1, Jg
Js J, Ja Jo J,o J,, J ,2 · J,3 J,,
0.00 1.00 -
0.25 0.98 0.12
-·
- 0.5
1.0
1.5
0.94" 0.24 0.03
0.77 0.44 0.11 0.02
0.51 0.56 0.23 0.06 0.0 1
-
2.0 0.22 0.58 0.35 0.13 0 .03
2.5 -0.05 0 .50 0.45 0.22 0.0 7 0.02
3.0 -0.26 0.34 0.49 0.31 0.13 0.04 0.01
4.0 -0.40 -0.07 0.36 0 .43. 0.28 0.13 0.05 0.02
s.r,
6.0
-0.18- 0.33 0.05 Q.36 0.39
0.15 -0.28 -0.24 0.11 0 .36
0.26 0.13 0.05 0.02
0.36 0.25 0.13 0 .06 0.02
-
7.0 0.30 0.00 -0.30 -0.17 0 .16 0.35 0 .34 0.23 0.13 0.06 0.02 - '
8.0
9 .0
0.17 0.23 -0.11 -0.29 - 0.10
-0.09 0.24 0.14 - o·.10 - 0.21
0.19 0.34 0.32 . 0 .22 0.13 0.06 0 .03 , -
10.0 -0.25 . 0.04 0 .25 0.06 - 0 .22
0.06 0.20 0 .33 0.30 0 .21 0 .12
-0.23 - 0.01 0.22 0.31 . 0.29 0.20
0.06 0.03 0.01.
0.12 0.06 0.03 0.01
.
12.0 0 .05 0.22 0 .08 0 .20 0.18 - 0.07 - 0 .42 -0.17 -0.05 0.23 0.30 0.27 0.20 0.12 0.17
-0.01 0.21 0.04 -0.19 - 0.12 0 .13 0.21 0.03 -0.17 -0.22 -0.09 0.10 0,24 0.28 0.25

,,,.
 I lYPES OF MODULATION
43

of order n but not in a simple way. Fig. ·

(ii) The I coefficients, in generctl, decrease with incrr.ase .
of zero and diminish gradually. Each J coefficient
3.6 shows that the ~alues of J fluctuate on both sides and
sideband terms. Hence the amplitudes of the sideb
represents the amplitude of the corresponding pair of
e of"· The modulation index S (or m ) thus determines
terms also evt!ntuaU~ d~re ase b~t not past~ ce~ in valu having amplitudes at least 1% of1the unmodulated
the n~ er ~I the significant sidebands, ,.e. sidebands
carri~r amplitude Ve.
(iii} • The sidebands at equal frequency intervals
fromfc have eq~al amplitudes. Thus the sideband ·
~·
distribution is symmetr
. .
ical about the carrier frequency. · , · . . .
.
. · (iv) . From Table 3.1 we find that as 6 incre
ases, value of any partic~la.r J coeffici~nt say 111 also
ulating frequency. Hence the relative amplirude of the
. increases. But 6 is inversely proportional to the mod . . . ·
ency is reduced.
distant sideband increases when the modulation frequ
and po~er and hence the total power
· . ( v) In AM, with the increase of depth of modulation, the sideb
d power remains con,$tant. However, with increased
increases. In FM, on the other hand, the total transmitte
width for relatively undistorted signal gets increased.
value of modulation index 6 (or m1), the required band
width required in FM is infinite. In
· (vi) From Eq, (3.46), it is evident that· the theoretical band
significant sidebands under most exacting condition.·
practice, however, bandwidth used is one incfoding all the modulation frequency, no significant sidebands
est
This implies that using maximum deviation by the high
are excluded. · ·

(vii) · In AM, the amplitude of the carrier com

ponent remains constant. But in FM, ihe carrier
•
component is J which is a-function of l> .-
0
.
(viii) · In FM, it is possible for the carrier com ponent to disappear completely. From Fig. 3.6 we find·
. . d
l to 2.4, 5.5, 8.6, 11.8 etc. These values of 6 are calle
· that this happens for values of 6 approximately equa--
eigen·va/~s.
to international regulations of FM broadcast;the
. Bandwidth and spec trum requ irem e.nt. Acco~ding
wing valu es are pres cribed: (z) Max imum frequency deviations.f.t= ± 75 kliz; (ii) Allowable bandwidth
follo
ier=± 2 kHz. From Table 3.1~ it is possible to find
per channel= 200 kHz ; (iiO Frequency stability of carr
for any specific value of modulation index 5•.•Thus
the magnitude of the carrier and -~ch sideband term
frequency deviation is± 75 kHz , the de~iation ratio
considering the modulating frequency of 15 kHz•. if the
lved in representing the carrier and the .sideband terms
6 = 75/15 = 5. The Bessel functions that are then invo h
(5) wher e n varies from zero to infin ity. Valu e of J (5) as a function of n may be obtained from grap
arel. · ,
0
• · · .
Fig. 3. 7.
such as in Fig. 3.6. Ju(5) as a function of n is_plotted in

. -v~
0·5
J~(S}
0-•

\
0·3 . '~
0·2 ,\
I
In (sl 0:1 .........

0 ,, 5· 6 .,!"'-.8 9 Ul 11 1.' n 1
-O·J
1

I
3·
' ' n-~

\ I
\. V .
.. .
Fig. 3.7. J,. (5) as fvnctlon of n.
44
- ...
-ltis found from Fig. 3.7 that/0 (5) is about-0.18 implifying th3:t the ~ier is about 0.18 Ve• Si .
11 (5). is about -0.33 implifying that the first order sideband terms have ampl!tudes of 0.33 Ve each. F
J2 (5) is very small, being about+ 0.05. Further 13 (5) is about 0.36 and _I• (5) is abo~t 0.39 • Beyond the
order sideband terms, the amplitudes of the sideband terms fall off ra~1dly and_ all sideband te~s bey
eighth have amplitudes Jess than 1% of the unmodulated carri~r amplitude Ve, i.e. they are not ~1gnifi
may be neglected.' For deviation ratio of 5, the signif}cant s1deban~ terms extend upto the eighth, i.~.
x
8 15 = 120 kHz on either side of the carrier for modulating frequency of 15 ~Hz.

. f.
~- v,
::, ' Carrier
.'! ::
a.
E
~

8 7 6 S 4 3 2 1· 0 1 2 3 G 5 6 7 8

L ·
~ -;t1Wml--
Fre quency
Signif1can1 ba n dwidth 2G 0
► . ,
kc/s--..l .
Fig. 3.8. Plot of lrequency spectrum of frequency modulated vo ltage fo r 6 • 5 and fm .. _15 kHz.
..
Fig. 1.8 s~ows the plot' of frequency spectrum of the frequency modulated voltage for 6 = 5
modulatioh frequency/,,. =·15 kHz ·as taken from Fig. 3.7. The amplitudes of she carrier and the side
terms are plotted.against frequency disregarding the sign of the Bessel function as given by Fig. 3.7.
· · Fof a given carrier'v9ltage, it is of interest to see how the spectral distribution varies as the devia ·
ratio ais increased keeping a fixed value of modulation frequency/,,.. Fig. 3.9 shows this spectral distributi
for several values of deviation ratio S. '
. It may be seen from Fig. 3.9 that for~< 0.5 second, third etc. sideband terms are less than one per
of the-unmodulated carrier amplitude and hence may be neglected. For 8 < 0.5, even in frequency modulati
system only two sideband terms are produced. In general, however, 6 is 5 or more. Hence in practi
significant sideband terms extend upto eighth or higher.
· . In most of the F.M. communication system, however, maximum frequency deviation is prescribed.
is, therefore, of interest to study the spectral distribution of this fixed value of frequency deviation and diffe
values of modulation frequency/,,.. Fig. _3-.10 shows this spectral distribution.
'
It is seen from Fig: 3.10 that total bandwidth requirement is 2/,,.:; 8 fa for 6 = 0.25 and it reduces
~ for 3 • O.S. For higher values of deviation ratio 6, the total bandwidth expressed in terms of/" goes
reducing. Finally for a= 10, significant sideband terms extend only slightly beyond'"' resulting in t
b_an~width o~ly slightly greater than 2/". thus keeping/, constant, total bandwidth required to include~
aigrufJCant sidebands, t.e. sidebands having ·amplitude greater than one per cent of unmodulated earn
amplitude, decreases gradually as the deviation ratio 6 increases and finally tends to equal 2ftt at cxtr~~cJYi
large values or deviation ratio 6. Fig. 3.11 shows the variation of n with deviation ratio 6, where n as
number or highest significant sideband terms. · • ·· · .
InP.M. broadcast, modulating signal has frequencies extending upto 15 kHz. At this highest modulatioll
frequency or 15 kHz with maximum frequency deviation of±7~ kHz deviation ratio 8.• 75/15 _.,5, The value
of n is then about 8 so lhat the significant bandwidth occupied ls 8 x 15 x 2 -= 240 kHz. This frequencY
bandwidth requirement ii rather large. At a lower modulating frequency, say 0.75 kHz, 8 = 75 kHzl().7S ~!!!
• 100 and the value of n is also about 100. Then the bandwidth requirement is ::a: 2 x 100 x 0.75 = 1~0 ~--
only, l.t. just about twice the maximum frcquen_cy deviation. In F.M. broadcast, however, the amplitudes of
. .
· TYPES OF MODULATION • ~5

r·
CARR1Eq
. . W,j CARRIE R I • ~ •C ZS
SIDfBANOS (6: wm' LOWER ., AMPLITUDE' . UPNa:11•:
•• f»T(),7 I."'.' SIOEBANO --- -:-- ---
. _
L-
. , -ie:~s4 r ·•
- _.:..,_·_ _ _..:... ..:_~
~
--- :---
.-l wd• ~•n, ___ ___ j _.

l -
I I
~
£ 6•2·0

6=-20
... d111l1,i... . ..-I) : 3·0
--l Wd: 2W,n h-

IL I, LIit. e I ,I / L.L. LJ •/ I.', ,

1. •\ .!~ 6: !) 0

~Id It
-j Wd =51£.n/--
. .
••11ll,.11,1,L1,11 .. ll1,. . s .,,o-o
. ,1111111,1 LLI, I.I Id 1111& ,. 'i, ; 1 0•0 -.jwd~,c .,.,,I-- · .
Fig. 3..,1 o. Spectral distribution in a frequency modu-
Fig. 3.9: Spectral ·distribution in frequency.modulated
lated voltage for fixed valu_e of frequency modulation
. voltage for a fixed vafue of modulating frequency fm
and different values of deviation ratio 6. f; and different values of modulation. frequency r,,,.
er than the amplitudes of frequencies in the
modulating frequencies beyond about 7.5 'kHz are much small
ncy deviation due to these higher sideband
middle and the lower frequency ranges. Consequently the fr~ue
significant bandwidth due to these higher
terms is much less than the permissible value of 75 lcHz. The
2/4, i.e. 150 kHz. In fact, the amplitudes of
moduiating frequencies, therefore, does not materially exceed
tion is s9 low that i(is found desirable and
higher modulating frequencies are so low and the resulting devia
frequency terms in order to raise the signal
often necessary to accentuate or boost up these higher modulation
and hence raise the signal/noise ratio. The noise
power remai!ls unaltered since the· noise power
. 10 •

generated within the circuits is uniformly dis-

tributed over the frequency band. Iri. FM ~

receiver, it is necessary 1 to de-emphasize the t .10, :.: . ·.f jl·. -:.:

I · · : · ·
signal after demodulaticm 'to regain the original , -:-:: -r ( J;,--f~-t~mF- .--r
ener:gy distribution. II . .I 11\ :
I I .-h '. I I ,.H ,, ~~I
-tJlf.
_ A thumb rule called Carson's rule states 10 0::: 1 •t''l:-: J

that as a go<,>d approxima tion, the bandw idth

sum
··f
. • .
."·:l .
i i:lfF.: -·t
~l+/l .r-".
required to pass an FM signa l is twice the
of the· deviation and the highest modulating • 1 • ijif . . .L I

frequency. Thus if the frequency deviations±75 I 10 10 2

kHz and the maximum modulating (requency is Gf'tMT.ICW /i;4TIO ~ ~

15 kHz, the required band width as per Carson's
rule equals_2(75+J5) = 180 kJ-fz. Fig. 3.11. Variation of n (order of highest sufficient-side-
band) with deviation ratio 6.

3.10. Phase Modulation. .

· · d ..
varying the phase angle of a carrier ~~ltage· in accor
. D~finition. Phase modulation consists involtage. · _a..cc
_with the msr.anr.aneous value of the modulating
red after phase modul~tion.
The a~pl!tude and frequency of the carrier voltage remains unalte
 .. RADIO ENGINEERlt(
. "

Expression for Phase M~ulated V9ltage,

Let the carrier voltage be, · "e = ve sin (roe t + 8J ••• (3.
and let the modulating voltage be, ~- = V
Ill M
sin coIll ·t
. . . \
.
l. · ·instantaneou s phase of the carrier before modulation is given by,

4>c:- =Cl)c I + 80
. ; . -·
After phase ~odul~tion, the instantaneous phase of the carrier.is given by.
·8 (t) = coc: I+ 80 + kP v,... . .. (3.S1)
=ooc: t + 89 + kp V,;. sin ~~ t ... (3.52)
The phase modulated carrier voltage is then given by,

f/ =Ve sin [coc: ·, + 00 + kP V,,. sin co,,. t] ... (3.S3)

. . .
In phase modulation process. the constant phase angle 80 plays no part ·and hence for the sake of
simplification 80 may be omftted. Then ~e modulated carrie~ voltage is giv_e n by. .

v ~ V~ sin [coc: t + kP V,,. sin co,,. t] ... (3.54)

• '
l~ •

The:maximum phase deviation obviously is le,,. 'V,,. and may be indicated by 4>,... Then the -modulated
voltage may be put as,
f/ ;:: Ve: sin [ro; I ,+ 4> sin ro,.. I] ... (3.55)
.
' .
111

or v = Ve sin [roe:,+ mP sin ro,,, tJ ·•·.. (3.56)

. where m,, ·= ♦,,. is the modulation index for phase modulatiori.

3.11. Co~parison of Expressions fo~ Phase Modulated and 1_4'requency Modulated Voltages
· Eq. (3.55) for phase mod~lated voltage is identical with Eq. (3.44) for frequen~y modulated voliage
or
except that instead of deviation ratio B( m1) in frequency modulation, we here have maximum phase deviation
♦,.. Accordingly the frequency spectrum of the phase .modulated voltage is similar to that .o f frequency :
modulated voltage. But the difference is that: ·
hi phase modulation

In frequency modulation :

·.•. (3.58)

' ..
From Eqs. (3.57) and (3.58) we see that in p~ase m~ulation, phase deviation ,. is independent of
modulating frequency/- whereas in frequency modulation, deviation ratio 6 is inversely proportional to .
modulating frequency / •. Hence in phue modulation, for all values of modulating frequency, the phase
deviation ♦• remains constant. However, for any single modulating frequency/,,.. the spectral distribution is

- li~. similar to thilt in frequency modulation, i.e. the sideband terms appear at interval of/,.. and have similar relative
 TYPES OF M~DULATION
47
I~ order ~o compare the e~fect of v·ariation of ~adulating frequen~y in the cases of frequency lllld phase
modulauon, we tak~_the followmg illustration: Let 4>.,. in the case of phase modulation be adjusted to be 750
!'8dians. Evidently thi_s situation for phase modulation corr~sponds to the co~dition of deviation ratio 6 = 750
· m fr~ue?cy m~ulat1on. 1;,et this deviation.ratio li = 750 be obtained at a modulating frequency of 100 H,z.
The s1g~1ficant sidebands m frequency modulation will then extend upro 750th order. · In both the phase
... , . modu~uon as well as frt;<tuency modulation, the significant bandwidth at modulating frequency of 100 Hz
occupied by the channel 1s 2 x 750x 0.1 = 150 kHz. If now the modulating frequency is increased to say the
maximum modulating frequency of 15 kHz, keeping V,,. constant; then in phase modulation~... still remains
unaltered at the value 750 radians and significant bandwidth occupied by the channel is =· 2 x 750 x 15 =
22,500 kHz. On the other hand, in frequency modulation, for modulating frequency of 15 kHz keeping V.,.
unaltered, the.deviation ratio 6 reduces to (750 x 0.1 J 15) = 5. - For this value of deviation ratio 6 =5, the
· significant sidebands in frequency" modulation extend upto the eighth order. Hence the significant bandwidth
·occupied in frequency modulation with modulating frequency of 15 kHz is= 2 x 8 x 15 = 240 kHz. This
bandwidth is very small as compared with the bandwidth of 22,500 kHz required in phase modulation. Thus
· it is concluded that keeping the amplitude V.,. of modulating voltage constant, as the modulating frequency/,,.
is increased, the significant bandwidth in phase modulation increases proportional to the modulating frequency
whereas in frequency modulation the bandwidth requirement increases only slightly. Stated otherwise, in
phase modulation the significant bandwidths do not converge as the prder of modulation fre.qucncy is increased
, whereas in (requency modulation, tne significant, sid~bands converge rapidly inspite of increase of modulating
frequency.- _:This constitutes one significam advantage of frequency modulation over phase modulation. · It
·maybe noted, however, that if V,,. is varied to keep o and ~"' identical for all modulating frequencies, then
both freq~ency modulation and phase modulation produc~ idel)tical sideband_s;

. From Eqs. (3.57) and (3.58) it is seen that expressions for oand~... for FM (frequency modulation) and
PM (phase modulation) r~pectively· are exactly ·similar in form except that the term· ro,., appears in the ·
deno~inator of expression for o. This provides a simple means of converting PM to FM. _All that is required
to be done is to convert the modulating voltage to a fonn where ro.,. appears in the denominator and then to
use this modified modulating voltage to ph~e modulate the. carrier. Ter~ c.o,,.· may be made to appear in
denominator of the exp~ession for modulation v_oltage by simple integration .. This principle has been utilised
in the Annstrong method of frequency modulation._ _· · ...., ·

The above considerations lead to the following practical effect : If an Bisignalis rec~ived on a PM
· receiver, the bass frequencies have considerably more deviation (of phase) than a PM transmitter would have .
·given them. The output of a PM receiver is.proportional to phase deviation. Hence the signal would appear
bass-boosted. Alternaµvely J>M signal received by an FM receiver would appear to be lacking in bass. This
deficiency can, of course, be corrected by bass-boosting of the modulating singnal prior to phase modulating.
This forms the·practical difference between phase modulation and frequency modulation. But it is quite
evident
. that one type.
of signal can be obtained from the other very simply. . .
' .

. Example 3.16. A 20 MHz 5 V carrier is modulated by a 500 Hz sine wave. The ma.xlmumfrequency
deviation is 15 kHz and the_same modulatio~ index is obtained/or both FM and PM. Write expression for
this modulated wave for (a) FM and (b) PM. Next if the modulating fre_quency is increased to 3 Hz, other
things remaining the same, write new expressions/or (c) FM and (d) PM. ·

.Solution. The carrier frequency ~c and the moduhJtion frequency ro,,. in radians/sec are : ·
. 6 • . .
roe = 2 7t x 20 x 10 =1.25 x 10 radians/sec . ·

ro,. = ?re x 500 = 3I 41 radians/sec.

 48 RADIO ENGINEERINQ
.

_The modulation index is, I

m =m1 =m,,
15000 = 30
500

Hence th~ expression for_FM wave is,

V =5 8
[1.25 X 10 t + 30sin 3i4J t]

~e. expression for PM wave is,

8
v = 5 [1 :25x10 t+30sin314 1t].

, - The two expressions are identical since m1 = :mp. When the modulation frequency is increased from
500 Hz to 3 kHz, i.e. made 6 times, the modulation index mP for J:>M remains unaltered whi1e...the modulation ·
index m1 for FM reduces 6 fold (from 30 to-5). Hence tqe·revised expressions for modulated carrier voltage
are: - · ·

FM: 11 =5 [1.25 x10 8

t + 5sin 3141 i]
8
PM : f/ = 5 [1.25 X 10 ' + 30 sin 31 41 I].
3.12. Comparison of Frequency Modulation and Amplitude Modulation
The frequency modulation has the following advantages :
(I) The amplitude of the freq~ency modulated wave is independent of the depth of modulation
whereas in amplitude modulation, his dependent orr the modulation index. This permits the use of low-level
modulation in FM transmitter and use of efficient class C amplifiers in al l stages following the modulator.
Further since all amplifiers handle constant power, the average power handled equals the peak power. In AM
transmitter, the maximum power is four times the average power. Finally in FM. all the transmitted power is
useful whereas in AM, most of the power is carrier which does not contain any· information.
(2) In FM there is a large decrease in noise and hence increase in signal-to-noi se ratio. This results
-from the following two reasons: (a) there is· less noise at carrier frequencies at which FM is used (typically
VHF and UHFJ and (b) FM 1eceiv.e rs can use amplitude limiters to remove all amplitude variations caused
by noise. ·

(3) • In FM noise may be further reduced by increasing deviation. AM does not possess this feature.
(4) International Radi_o Consultative Commjttee (CCIR) of the I.T.U. allows for a guard band
between commercial FM stations. Thus there is less adjacent channel interference than in AM. .
.
(5) FM broadcast transmitters operate iri the upper VHF range and in-the UHF range. At these
. than in the MF and HF ranges used for AM broadcast..
high frequencies, there is less noise
(6) Since FM broadcast taJces place in the VHF and UHF ranges, the propagation used is space
wave propagatwn. The radius of operatiQn is limited to slightly more than the line of sight. This permits _use
of several independent FM transmitters on the same frequency with negligible interference. This.is not possible
· in AM.
..
The following are the disadva_n tages of FM :
(1) A much wider chann~l typically 200 kHz is needed in FM as against only 10 kHz in AM
oadcast. This forms !lerious limitation of FM. ·
~-"""Ila...
(2) . . FM transmitting and receiving equipments particularly for modulati_o n and demodulation tend
more complex anct hence costly. ·
•
 TYPES OF MODULATION 49
• .
: '(3) In_ FM, the recep tion using conv · l . . . · .·
th 1
!11~ ~ s lumted to hne of sighL . Thus the FM area of
. reception of FM 1s much smal ler than for FM Ten.bo na
. due to the cani er frequ encie s (in VHF and U h1_s restnctlon is not du~ to the intrinsic properties of
no doub
but
t, a
disad vanta ge for FM mobi le communicati HF range ~ emp loy~ for us transmission. This is,
hanne l allo.-
- cations.. . _ ons over 8 wide area but forms an advantage for to-<:=

Mod ulati on . _
~-~J. Noise and.Fr.equency
tha0 AM d · · •ri • · · · · ·,
FM is much more imm une to noise. _an is sigru icant ly more immu ne than phase modulation.·
We hereu nder exam in th lish the above facts and to· determine the extent
. . e e effec t of nmse on a earne r to .,estab
.
of__noise 1mprovemenL
.J.13.1. EfTect of Noise ori Carrier : Noise Triangit
•· Cons ider a si~gl e nois~ f~equency .- It will affect ' .. • I

-- --
the outpu t of a rece1ve_r only 1f 1t falls within its pass-
b~d. In that c~e. the earn er and noise voltages will
!"IX and th_ e diffe rence ~requency, if audible, wilJ · . We ,

mter~ere . with th~ recep uon of the wanted signal.

C~ns1denng the smgl<: noise volta ge vectorially, the
noise v_ec~~ gets supenm{>Qsed on the carrier, rotating
aoout .1t with retau ve angu lar velocity (w,. - -we) as
_shown in Fig. 3.12. The maxi mum dev'fation in the Fig. 3.12. Vector effect of noise on carrier.
resultant ampl itude from the avera ge -value is V
whereas µJe maxi mum , phas e deviation ii
41 =sin- (V,. I Ve) .
1
=•

Let the ~ oise volta ge w_npHtude be one~fourth of th~ c.arri

er voltage amplitude. Then for Ai\1, the ·

deviation is c)> = sin 0.25 / 1 = 14.5°. We assume

modulation m. = V,.! Vc =·~= 0.25 while the maxi~u~ phase
:md does not respond to ph~ changes. We .f~e r
here that AM recei ver respo nds only to-amplitude changes
changes and does '!_Ot respond to amplitude c~anges
assume that the FM recei ver respo nds only to frequency
amplitude vari~tions; We now proceed to assess
since the ampl itude limit er in FM receiver re~o ves all the
of a amplitude changes on AM receiver. _ : ·
.the influ ence of phas e ~hanges _on FM/ ~eiv er and that
for FM. Let the mod;ula~ing frequency be
We make this comp ariso n unde r the most severe condition
modulation index for both AM and FM be unity.
15 kHz and let us assum e for the sake of simplicity that the be 0.25/1 = 0,25. Concerning FM, we convert the
Then in AM recei ver noise-to-signal voltage ratio will
ratio is 14.5°/57.3° = 0.253 . Thus the noise-to-signal
modulation index from unity devices tcfradians. .Thus the . · ·
· ·
ratio in FM is just slightly worse than_in the case of AM.
ency has been altered fro_m 15 kHz to th~
We next study the perfo rman ~ when the modulation frequ
frequency (ro,. - ro~) and the m~u latin g frequency_
lowe st val~e say 30 Hz. In AM, as the noise difference
ence in the relative _noise, carrier and the modulating
are reduc ed from J 5 kHz. to 30 Hz, there appears no differ
noise and modulating frequencies do not vary the
volta ge amplitudes. In other word s in AM variation in the
ratio of noise to carrier vqltage remains constant, ·
noise -to signal ratio. In FM, on the other hand, since the
due to noise -also remains constant. Thus while
the value of modulation index, i.e. maximum phase deviation
noise sideband frequency is reduced), the modulation
them odul a•.ion index due tonoi serem ainsc onsta nt(as the
to the r~uc tion in modulation freqµency. Hence
· indei cause d by th~ signal goes on increasing in proportion
modulation frequency. At the lowest modulation
in FM, the noise!to-signaJ ratio goes on reducing with
3 x 30 / 15000) =,0.000505. · Thus the noise-tQ:'---,,
frequency of 30 Hz, the noise-to-signal ratio in FM is (0.25 -
per cent at 30 Hz.
signal ratio reduces from 25.3 per cent at 15 kHz to 0.05
spread across the pass band of the receiver.
We assum e the noise frequency components to be evenly
decreases uniformly with noise sideband frequency · _
. Henc e it is evident that the noise outpu t from the receiver
for FM. On the other hand, in AM it remains constant. Fig.
3.13 (a) illus1rates these noi5e fideb and distributions
is· referred _as to the noise triangl~. The noise
for AM ~d FM. The triangular noise distribution for FM
-9
 ••I •
50
•
sideband distribution fer A.M is a rectangle as shown in Fig. 3.13 .(a). From Fig. 3.13 (a), we may
that the average voltage improvement for FM under these conditions is 3: 1. ~uch a conc~usion is v ·
average audio frequency at which FM nmse voltage appears to be half the AM nmse voltage. .m actual Pl'l
however, the sithation is more complex and the improvement obtainable in FM over AM is only a vo
ratio of~: 1, i.e. power ratio of 3 : 1 or about 4.75 dB. · ..
~ We have as~umed in the beginning that the noise voltage is lower than the signal ~oltage. Wh~
signals ?fe simultaneously received, the amplitude limiter gets actuated by_the stronger signal ~d it tends
reject the weaker signal. Accordi..gly if peak noise voltages exceed the, signal voltages, the signal will
excluded by the limiter. With very low signal-to-ooise ratio, therefore, AM is superior to FM. Thee
value of signal-to-noise voltage raLio at which FM becomes superior to AM depends on the value of
moduiation index . . However, in general, FM becomes superior to AM when signal-to-noise voltage
becomes 4 (12 dB) or more at the amplitude limiter level. ·

fc Rectangular
. distribution
· AM.
FM .Noise
Triangle .

(a) mFf at maximum frequency. (u) m~5 at maximum frequency.

. · Fig. 3.13. Noise sid~band distribution in AM and FM.
Noise Triangle for m1 > 1. In AM, the maximum permissible value of m,. = I. In FM, th.e re is no such
limit. In FM, the limit is on the maximum frequency deviation. Thus for FM VHF broadcast, maximum
frequency deviation is limited to75 kHz. Hence using even the highest modulation frequency of 15 kHz, the
modulation index in FM broadcast is as high as 5. At lower modulating frequencies, the modulation index is
correspondingly higher. Thus with modulation frequency of 1 kHz, m1 is 75. The signal-to-noise voltage
ratio in·the output of the limiter in FM receiver will get increased in proportion to the modulation index. Thus
with m1 = 5 (the highest permitted m1 f()r f,,. =· 15 kHz), the signal-to-noise improvement is 5 : l in voltages
and 25 :. 1 in ~wer (1~ dB). No such improvement is possible for A~. With sufficient signal-to-noise ratio
at the receiver input as assumed earlier, overall improvement secured in FM over AM is (4.75 + 14) = 18.15
DB. Fig. 3.13 (b) shows the noise triangle for m1 = S: ·
From the above consideration it becomes evident that in FM, we may use reduced bandwidth and
thereby achieve higher signal-to-noise ratio. Such a trading of bandwidth is not pos.s ible in, AM. It may ~so
be_noticed that just the increase of deviation (and hence ·the system bandwidth) in FM, does not neces~ly
mean that more random noise will be admitted. In fact this extra random noise produces no effect if the noise
sideband frequencies lie outside the passband of the receiver. Hence from this consideration, the maximum
· deviation and hence ban(lwidth, may be increased without fear. Phase modulation also has all the properties
of FM except the noise triangle. Noise now pha5e modulates the carrier but there is no improvement as
modulati11g and noise sideband frequencies are ·lowered. Thus under identical conditions, FM will be 4.7 ~
- ~terthan PM regarding noise. It is for this reason that frequency modulation is preferred to phase modJiauon ·
111 practical transmitters. · ·
. ' . .

In practice, however, in FM, bandwidth and maximum devfation cannot be increased indefinitely. 'fhUS
when a 1;>ul~Js a~l_ied to a tuned circuit, i~ peak amplitude is proporlional to the square root of the bandwidth
ft~ circuat. S1mdarly when a noise impulse is upplied to the tuned circuit in the IF amplifier of an~
rec~•v~. a large noise pulse results bccau:!>e of the unduly large bandwidth needed to·accommodate the high
deviation. When Lhe maguitude of noise pulse!) e>.ceed about one-half of the carrier amplitude at the amplitude ·
. '
• ,VPES OF MODULATION
51

li~iter, then .the limi~ ~uncti~n fails. Wh~n _the noise pulse ma~itude exceeds the earner ~plitude, the
noJ.Se so_to sa_y; captures ~e signal. The maxunum deviation of 75 kHz is a compromise between the two
extreme condtUQns descnbed above. · · ·
. . . .

· : It may be proved that whe~ impulse noise amplitude V,. < O.S Ve, this i~pulse noise get~ red~ced in FM.
to the ~e ~xtent as ran~om noise. ~M; c~mmunication receivers use amplitude H~iters. Such a limite~
does not linut random noise at all and lmuts &mpulse by about 10 dB. Thus the FM system is better than the ·
AM system in thi~ regard as well. · ·

. J.13.2~ Pre-e~ phasis and J?e-em phasis. The noise triangle of Fig. 3.13 shows thanh~ noise produ~es
greater effect on the higher modulatmg frequencies than on the lower ones. It is, therefore, considered desirable
that the higher modulating frequencies be artificially ~tcd up at the transmitter before modulation and
correspondingly cut at the receiver after demodul.ation. Th.is greatly improves the noise itnmuriity at these
higher modulation frequencies. This boosti~g of the higher modulafion frequencies.at the transmitter fn any .
desired manner is called pre-emphasis while .the relative attenuation of these h~gher modulation frequencies
at the demodulator output _in the receiver is ·called de-emphti.si.s.
. . .
Fig. 3:14 (a) shows a :typ~cal pre-emphasis circuit while Fig. 3.14 (b) shows the corresponding de-
emphasis.circuit The pre-emphasis in USA FM broadcasting and in the sound transmission accompanying
television. has be.en standardized at 75 µs whereas.several other services, such as European and Austral_ian_
-broadcasting and TV sound transmission, use
pre-emphasis of 50 µs. When using 75 µs pre-emphasis at
ttansmitter, corresponding 75 µs de-emphasis must be used at the receiver. This is necessary in order that
the relative amplitudes of the mod(!lation freque~cy .terms unaltered. Fig. 3.14 (a) shows ·an L-R circuit of
timeconstantL/R = 50 µs used for pre-emphasis while Fig. 3.14 (b) shows a C-R circuit of time constant RC
·= 50 µs used for de-emphasis. These values of L, R and C may be altered to obtain pre-emph~is and
de-emphasis of 75 µs . A 50 µs pre-emphasis corresponds to a frequency response which_ is 3 dB up at the
frequency whose time constant RC is 50 µs. This frequency is given by /=Rl7rcL and 1s, therefore 3180
Hz. Fig. 3.15 shows this pre-emphasis curve for 50 µs A ~0 µs de-emphasis corresponds to frequency resJX>nse
·at
which is~ dB down the $&me frequency 3180 Hz (3 t 80 Hz= 2 ,/Rc}
Fig 3.15 sh~ws this de-emphasis ~urve
also for 50 µ.s~ The corresponding frequency for _pre-emphasis.of 75 µs . is 2120 Hz. ·:- .
• ~ ' I
s

, : !-

f Ver.: ttl
.. )j, •
r~~ Sous ~ ~-SOH •· •· . , ~ . , . Cc

A i 10.k fl:
Cc
. Pre-•mD~~siz,d
R.F From · ·
·~~~ft--, ,,-,_.-Oe-.:mphas1zed
L:,_. acdio .o utput·
: . I· ,.,...~----o . O~modulator c-['"' .
· ~· Pre-emphas•z~d J_ RC =SOflS
L audio o!,ltj:>ut '
.Mu~ulo~,o~s . .

,.
(a) Pre• ,mphasis (b) De-emphasis

· Fig. 3.14. 50-µs pre-em_p~asls and de-emphasis circuits.

 •
52 DIO ENGINEER!
AA_
•
The role of pre-emphasis ·m ay be seen as below :
Let there be two modulating signals ha .
the same initial amplitude. · Let one of these
---"------- higher fre:ciue~cy) be pre-emphasized tosayt ~
, PRE-EMPHASIS -
the amplitude whereas the other (at lower
quency) be left unaffected. Then the receiver .
n~turally de-emphasize tfie first signal by raci
2 m order t<? ensw:e that both the signals have
same amplitude m the· output of the receiv
However, before demodulation, i.e. whiles!
ceptible to interference by noise the emphasi
signal has twice the deviation it would have :
· ~ithout pre-e!31phasis and is, _therefore, ~ore
immune to n01se..

Subjectiv_e tes~s have shown that 50 µs ·

Fig. 3.1_5: SO µs pre-emphasis and de-emphasis curves.
emphasis gives ·an improvement of about 4.5 dB in signal-to:noise ratio- an9 relatively greater improvement
with 75 µs emphasis. Care must, however, be taken that . the: higher· modulating · frequencies are not
over.:em phasized, or else over-modulation rhay take place with frequency deviation exceeding 7 5 kHz resulting
in disu,rtion. In. practice, the order of pre-emphasis used is a compromise between protection far high
modulating frequencies on one hand and the risk of over modu!ation O!} the other. Pre-emphasis may as well
be used in AM This results in some· improvement but not as great as.in FM; since the modulating frequencies
in AM are.not unequally 'affected by noise. . ·
. . . .
• 3.13.3. Other Forms oflnterference. Apart from noise~ other forms of interference are found in radio
receivers-sµch ~ (1) image frequency, (ii) transmitters operating on an adjacent_ channel and (iii) transmitters
operating on the same channel. The first of the above mentioned interference is discuss~d later. The other
two types.are discussed here. . 1
•

Adjacent Channel Interfere.,ice. FM provides not only improvement in the S/N ratio but also greater
discrimination against all other interfering signals, no matter what their sourc~. We have already seen in the
preceding section that FM with maximum deviation of 75 kHz and 50 µs pre:emphasis provides noise rejection
of at least 23 dB beuer than AM. Accordingly if an AM receiver needs S/N ratio ·or 60 dB at the detector for
. excellent performance, then an FM receiver will provide the same performance for SIN ratio of qnly 37 (= 60
- 23) dB. This results irrespective of whether the i,n terfering signal is due to noise or ad~acent channel signal.
The mec~anism of FM limiter of reducing interference is exactly ~he sarriel~hether i\ is ~oise or a~jacent-
• -channel signal. . - . ·
Furlher each FM broadcast channel occupies 200 kHz. Out of this, only I 8d kHz is actually used while
lhe remaining 20 kHz constitute the gu~d band which redu~es adjacent chann~I interfer~nce_further.
Co-channel Interference. The amplitude limiter used in FM receiver passes the stronger signal but
eliminates the weaker one. It is for this reason, as mentioned earlier, that noise reduction is obtained in~
provided that the signal is at least twice the ·noise peak amplitude. ·For the same reason, a relatively w~aket
~nterfering signal from any other transmitter operating on the same frequency as the desired one, will be .
attenuated.
,,, Thus co-<;hannel interference is suppressed in FM. ·
The possibility of co-channel interference arises in practice when a mobile r.eceivcr travels from one
trdnsmiu.er towards another operating on the same frequency. Interesting phenomenon of capture takes place.
Thus in r-M as the mobile rccei vcr moves from one tmnsmiuer to the second, the second transmitter is virtually
inaudible ~using practically no interference so long as the signal voltage from the sec_ond transmitter i_s less
the
than about half of tha1 from the first. Beyond this point, the second transmitter becomes quite audible m_
b~ground and eventually pr~ominatcs thereby excluding the first transmittc~. T~us the mo~ile receiver
•gc_L~ captured by the second transmiucr. When the receiver is in the transition reg1on'.1.e. roughly m the centre
 •
TYPES OF MODULATION 53

• ·. ··
1,0ne and fading takes place then signals fi O the two transmitte rs are alternately stron ger. Thus the rece1 ver
. al b ' . r m mitte r to the other · •
1 then the other. This switching from one trans
IS captured t~mate Y Y one transmitter and - .
is most annoymg and does not happen in AM system. -
' - ! 0 is
AM receiver capture effect not obtainable. In thispredo
d always
case, as the mobile receiver travels from one
minate while the other one would be heard
P.BJIS!Jllt~r t? the ~on d, the nearer transmitter woul distant ·
as q01te s1gru~cant interference although it may be very
band FM is one in which the modulation index
: 3.13~4. Wid eban d FM and Narrowband FM. Wide
been discussed. . In wideband broadcast FM the
nonnallx_·exceeds unity. This is the one which has so far
the maximum permissible.deviation is 75 kHz. ·
modulatltig frf';luencies extend from 30 Hz to 15 kHz w~ile
2500. In narrowband FM, the modulation index is
Hence the maximum modulation index.ranges from 5 to
ency is usually 3 kHz and the maximu'm deviation
· usually about u~ity sfocc the maximum modulating frequ • ·
is usually 5 kHz. . . . . .
application. Large frequency deviation and
The bandwidth used in any FM system depends on -the
is better suppressed. Care must, however, be ~en
consequent large ban~width has the advantage that noise
to ensure that impulse noise peaks do not beco
me excessive. Wideband FM systems however, need large
system. · From these considerations, t~e wideband
bandwidth, typically 15 times that of narro\\'. bandwidth
eas narrowband FM systems are used for commu-
FM systems are used in entertatnment broadcasting wher
communication -services such as police. wireless, ·
nications. Thus narrowband FM is used by the mobile
es and defence. In all such cases, higher audio
ambulances, taxicabs, short range VHF ship-to-shore sourc • .1
telephone services but the resulting truncated speec_h
frequencies are attenuated as in the case of Jong distance
tion permitted in such services ranges from 5 to
is still perfectly clear and intelligible. The maximum devia
are sometimes used. Pre-emphasis and de-emph_aliis
IO kHz. Narrowband _system with even lower deviations ·
F~ systems.
are used in such narrow band FM system afso, as in other
o FM system, enough infonnation is s_ent to
3.13.S. Stereophonic FM Multiple~ Systems. In stere
material. Such a stereo FM system came into com-
the receiver to enable it to reproduce the original stereo
ural FM system. This stereo FM system had to
'mercial usage in 1961, several years after commercial mona This resulted in an unduly complicated stereo_
system.
• · be made compatible with the existing monaural FM
s~ste m straig htway, ~e sys~em w<?uld have been considc~ably
FM system. Had we switched to FM stereo_
sr~~em _m wh1ck_c~lou.r TV ca.~ e later .than the
simpler. · The situation is similar to that e~1sung for TV_ hty with the ex1stmg_commercial monaural FM
monochrome TV. Thus from the consideration of compat1b1
nel system with a left channel and a right channel
system, it is not possible in stereo FM to use a two chan ·
transmitted sim~ltaneously an~ independently. .
ultiplex generator with optional SCA an~ follo_ws
. · Fig. 3: 16 ·gives the block diagram of the stereo FM _m
channel -outputs Land Rare fed lo a matrix-which
the standards laid down by FCC.in 1961. Here the two
The sum signals _(L _+ R) of frcque~cy-5~ Hz l? 15 ·:
produces sum (L + R) and the difference (L -R)_ sign~ls.
kHz modulates the carrier in the same way as the signa
l ma monaural trans.m1ss1on. The sum signal 1s rccc, vcd
ion and reproduced at its output as if it were the
by the monaural FM receiver tuned to the stereo transmiss ' ·
complete signal senL_ ·
o receivel 'and qn being added to the sum
.The difference signal (L -R) after demodulation ln a stere
renc~ between the sum (l + R) and the difference
signal (L + R) produces the left channelsignal while the diffe
(L -R) signals produces the right channel. We here
study as to how the difference signal is impressed on the
·
carrier.
py the same frequency range of 50 Hz to
·Both the sum (L + R) and the difference (l -R) signals occu
ls, being in the same frequency rµnge will get
15 kHz. If impressed together on modu:ator, these two signa
ency from 50-1 500 0 Hi to a higher vaLue.
mixed up. T_o avoi~ this ,~ ~iffcrence .~ignal is shifted in frequ rum is referred to as frequency multiplexing
spect
Such a stacking of signals m different parts of the frequ·ency
l amplitude modulates a sub-carrier at 38 kHz in a
and hence the name of this system. The difference signa
balm1ced modulator~ the subcarricr gets suppressed
su~pressed ~e r balanced modulato~. At the oulp~t of the
extend.upto. 15' kHz on either side of the sub-carrier
while the two sidebands alone are oblamed. These sidebands
54 RADIO ENGINEERING
of 38 kHz and thereby occupy frequency range extending from 23 kHz to 53 kHz. The sidebands.
to the sum signal ( + R) occupying frequency range 50-15000 Hz and a 19 kHz sub-carrier are
cornbincd signal then frequency modulates the carrier. No interference between the sum and thesignal. addedThis
channel signals thus occurs since they arc stacked at different frequency sloLs. This frequency dif erence
carrier is then transmitted and received in the corresponding stereo FM receiver. In the monauralmodul ated
receiver
the audio frequency band corresponding tothis difference channei (23-53 kHz) is filtered out and discarded.
In a stcreo FM receiver, on the other band, the wanted difference signal is extracted. To faciliate the a
exiraction of difference signal and the demodulation process, a sub-carrier of 15 kHz (half the suppesso
sub-carrier frequency) is used for demodulation. The sum and difference signals are then addedin on
combining network and subtracted in another combining network to yield the left and the right channels The
two Separate bands of signals are amplified in separate chains of audio amplifier and reproduced as the tuo
channels of the system.
Left
Channel SUM(L+R) S0 Hz-15kHz

DIFFERENCE 23-53 kHz

Right (L-R)
A dder Freq
Modu -
Channel fator FM
19 kHz
Qutput
59-5-74.5- 3
kHz

19kHz Carrier
Sub-carrier Freq. Suppressed SCA
Generator, 19 kHz
Doubler Balanced Audio Generat or
38kHz Modulgtor in

Fig. 3.16. Stereo FM Multiplex generator.

Stereo FM multiplexing used here differs from conventional multiplexing in the fact that here the lowest
audio frequency is 50 Hz compared with 300 Hz normally encountered in communication voice channel
multiplexing. This low minimúm frequency of 50 Hz makes it difficult to suppress the unwanted sideband
without affecting the wanted one. The second problem which arises is that it is difficult to extract the piot
carrier in the receiver. However it is imperative to-use some form of carrier to ensure that the receiver has a
stable reference frequency for demodulation failing which distortion of the difference signal occurs.
The 38 kHz sub-carrier is generated from 19 kHz oscillator for aspecific reason. Itavoids the difficulty
of haying toextract the pilot carrier from among the close sideband frequencies in the receiver. As shown in
Fig.3.16, the output of 19 kHz sub-carrier generator is added to the sum and the difference signals in the
output adder preceding the frequency modulator. This frequency of 19 kHz neatly fits into thespace becween
the top of the sum signal and the bottom of the difference signal and is at the same time far away from cach
of them. Hence there is no difficulty inextracting it in the receiver and also in suppressing the unwanted
sideband without affecting the wanted one, Thus both the problems mentioned above are overcome through
use of 19 kHz sub-carrier.
In the receiver, the 19 kHz signal is oubled in frequency and is then reinserted as thecarrier for the.
difference signal. This 38 kHz sub-carrier is reinserted at 10% level which level is adequate but at the same
time not so large as to draw undue power from the sum and difference signals or to cause over modulation.
 TYPES OF MODULATION 55

In the system described above, a Subsidiary Comununication Authorizaion (SCA) signa!

transmiued shown by dashed linc in Fig. 13.6. This SCA may then provide a second medium quality may also be
mission used as background music in restaurants, stores etc., The SCA trans1nission uses a sub-carrier ofrans
67
KHz frequency modulated to a depth of +7.5 kHz by the audio signal resulting in frequency band
from 59.5 to 74.5 kHz which fits in the frequency spectrum sufficiently above the extending
to inierfere with it. Fig. 3.17 shows the overall frequency allocation within the difference signai sO as not
modulating signal
stereo multipie transmission with SCA. Care has however, to be taken to keep the amplitude of the sumof an FM
the difference signalsabout 10% in the presence of SCA failing which over modulation of the main and
may result. carier

Sub-carrier

Difference Optional SCA

Sum channet
Transmission
channel (l- 2)
(l +R)

15 19 23 38 53 59.5 67 74-5
Aud1o FM Frequency
Double side bang
Suppressed (kHz)
Carrier AM

Fig. 3.17. Spectrum ot stereo FM multiplex moduiating signal with optional SCA.
SUMMARY

Modulaticn. Modulation is the process by which some characteristic, usually amplitude. frequency or phase angle
of a vcitage (called the carrier voltage) is varied in accordance with the instantaneous value of some other voltage, cailed
the modulating signal.
Amplltude Modulation. In amplitude moduiation, the amplitude of the carrier varias in accorda.ic with the
instari taneOUS value of the modulating voltage.
Modulating voliage = cos ,
Carrier voiage =V cos w, i
Modulated carrier voltage e=V[1 tm, cos , cos a,t

Modulation index : m, = Ve

Stdebands produced in AM

oV cos a, 1+Ve cos (a, +o,)1+ cos (a,- , )

Power Relations in AM : P, =P +Psa +Puss

Current in Amplitude Modulation

56 RADIO ENGINEERING
Modulatlon Index, This is the fraction by which the amplitude of the carrier changes an amplitude modulation
Frequency Modulatlon. Frequency modulatibn consist in varying the frequency of the carrier voltage in
with the instantaneous value of the modulating voltage. accordance
Modulating voltage:
Carrier voltage : =Vesin (o, t+0)
Modulated carrier voltage : v=V sin (o,1+m, sin o, 1)
Deviatlon Ratlo 8. It is the ratio of the frequency deviation to modulation frequency and forms the modulation ind
m, for frequency modulation.
K,.V.
Sideband Terms In Frequency Modulation. When a çarrier voltage is frequency modu!lated by a single sinusoidal
voltage , there are produced numerous sideband terms at intervalof modulation frequency a.
Slgnlficant Sldebands. In frequency modulation, significant sidebands are those which have amplitude at least
equal to one per cent of the unmodulated carrier ampitüde.
Phase Modulatlons. Phase modulation consists in varying the phase angle of the carier voltage in accordance
with the instantaneous vaiue of the modulating voltage.
Modulating voltage : , =V, sin o
Carrier voltage : , =V sin (a +0)
Phase modulated carrier voltage :
v=V sin (w! +0, sin o, 1)
Modulation index . =m, =k, Va
Merits of FM. () The amplitude of the frequency modulated wave remains unaffected.
In FM there is a large decrease in noise and hence increase in S/N ratio.
(üi) In FM, hoise may be further reduced by increasing deviation.
(i) In FM, frequency allocation allows for a guard band. This reduces adjacent channel interterence.
In the UHF bands where FM operates, there is less noise than in the HF or MF bands.
(v) FM permits use of several independent transmitters on the same frequency with negligible interference.
Disadvantages of FM. () Amuch wider channel, typically 200 KHz, is needed.
Transmiting and receiving equipments are complex and costly.
(ün Reception using conventional method is limited to line of sight.
Pre-emphasis In FM. In FM transmitter the higher modulatjon frequencies are boosted up before FM modulation
using typically 50 us L-R network.
De-emphasis. When pre-emphasis is used in FM receiver.at the output of detector, higher modulation frequencies
are relatively atenuated to bring them back to their original relative values. Use of pre-emphasis and de-emphasis resuls
in improved S/N ratio for higher modulation frequencies.
AdjacentChannel Interference in FM. In FMsystem, use of limiter results in automatic reduction in adjacent ohannel
interierence. Adjacent channel interference in FM is also reduced by the guard band pravided in FM broadcast channel
allocation.
Co-channel Interference ln FM. Use of amplitude limiter.in FM receiver results in intarference reduction provided
that desired signal channel is reasonably stronger than the undesired co-channel signal.
Wideband FM. Itis used for broadcast. Typicaly the modulating frequencies extent from 30 Hz to 15 kHz. Modulation
index exceeds unity. Maximum permissible deviation is =75 kHz.
Nerrowband FM. In narrowband FM () modulation index is usually about unity () maximum modulating frequeny
is USualiy 3 kHz and(ih) maximum frequency deviation is usually =5 KHz. It is used by mobile communication servicos.
Slereophonlc FM Multlplex System. It does not use two separate channals. Instead the sum of the two channals
ismonaural
sent as receiver
one signalandandreproduced
the difference as the other
at output. signal. The
The difference sumamplitude
signal signal modulates
modulatesthea FM carrier and
sub-carrier is kHz,
at 38 received by
which
sub-carrier is then suppressed. The sidebands extending from 23 to 53 kHz then frequency modulate the carrier along with
the sum signal.
TYPES OF MODULATION 57

REFERENCES
3.1. Sturley, K.RA. :"Frequency Modulated Radio, George Newnes Ltd., London, 1958.
3.2. Taub, H., and D.L. Schilling: "Principle of Communication Systems", McGraw Hill Book Company, New
York, 1971.
3.3.
Mandel M. :"Principles Electronic Communicaions", Prentice Hal lnc.,Eaglewood CHifls, NJ., 1973.
3.4. Kennedy G.:"Electronic Communication Systems", McGraw Hil Kogakusha Ltd., Tokyo, 1977.
3.5. Tarmans F.E. :"Electronics and Radio Engineering,McGraw Hil Book Company, New Yotk,1955.
3.6. Ryder. J.D. "Electronic Fundamentals and Applications,Sth edition, Prentice Hallof lndia Private Ltd.,
Naw Delhi, 1978.
3.7. Stremier, F.G."Introductión to Communications System", Addison Wesley ublishing Co., Reading, Mass.
1977.

REVIEW QUESTIONS

3.1. Define the term modulation.

3.2. What is meant by the term amplitude modulation ?
3.3. What is meant by the term frequency modulation ?
3.4. Define the term modulation index.
3.5. Write expression for the sinusoidal carriorvoltago which has bean amplitude moduiated by another sinusoidal
modulating voltage.
3.5. Prove that after amplitude modulation, the carrier power increases from P. to where m, is the
modulation index.
3.7. Define the term deviation ratio 8 in frequency modulation.
3.8. Write expression for the sinusoidal carriervoltage which has been frequency modulated by anothersinusoidal
modulating voltage.
3.9. Prove that in frequency moduliation, there are produced sideband terms extending theoretically upto infinity.
3.10. What i_ meant by the term "significant sidebands in frequency modulation ?
3.11. Write expression for the sinusoidalcarrier voltage which has been phase moduiated by another sinusoidal
modulating voltagY.
in
3.12. Prove that the significant sidebands converge rapldly inspite of the increase of modulation frequency
frequency modulation but not so in phase modulation.
3.13. What are the principal merits and limitatons of FM ?
3.14. Discuss the effect of noise on carrier in FM system.
3.15. (a) Why is it nacessary to employ pre-emphasis and de-emphasis in FM system?
(b) Draw typical pre-emphasis and de-emphasis circuits.
3.16. Explain how adjacent channel interference gets reduced in FM.
is stronger
3.17. Explain how co-channel interference gets reduced in FMsystem provided that the desiredsignal
than the co-channel interfering signal.
3.18. Give the salient features of wideband FM system.
3.19. Give the typial applications of narrowband'FM system.
3.20. Draw a block diagram and explaln the principle of stereophonic FM multiplex system.
NUMERICAL QUESTIONS

3.1. Asinusoldal carier voltage of frequency 10 MHz and amplitude 200 volts is amplitude modulated bya
sinusoldal voltage of frequency 10 kHz producing 40% modulation. Calculate the frequency and amplitude
of upper and lower sidebands.
(Ans. 10010 kHz ;9990 kHz ;40 volts]
3.2. The tuned circuit of the oscillator in asimple AM transmitter uses a coil of 20 H and shunt capacitor of
value 0.8 F. If the oscillator output is modulated by audio frequencies upto 10kHz what is the frequency
range occupied by the sidebands ? [Ans. 1248 to 1260 kHz]
58 RADIO ENGINEERING
800 kHz is amplitude
Asinusoidal carrier voltage of arnplitude 80 volts and frequencymodulated
3.3.
sinusoidal voltage of frequency 15 kHz resulting in minimum carrier amplitude modulated
of 72 by a
Compute (a) the sidaband frequencies and (b) modulation index. vols,.
[Ans. 785 kHz ;815 k
Asinuscidal carrier voltage of frequency 1 MHzis amplitude
kHZ.m,
modulated by a sinusoidal voltage ofi =0.1
3.4.
10 kHz resulting in maximum and minimum modulated carrier amplitudes of 85 and 75 volts frequency
respect
Calculate (a) the unmodulated carrier amplitude (6) modulation indexX and (c) amplitude of each sice ivel,
[Ans. (a) 80 volts (b) 0.0625 (c) 2.5 volh!
3.5. A sinusoidal voltage amplitude modulates another sinusoidal voltage of amplitude 2 kV.to resuh i
sideband terms each of amplitude 200 volts. Compute the modulation index.
(Ans. 02
3.6. The rms value of an RF carriervoltage is 100 volts. After amplitude modulation by asinusoidal audio voltage
the rms value of the carrier voltage increases to 108 voits. Compute the modulation index.
(Ans. m, =0.57
3.7. The rms value of an RF carrier voltage is 80 volts. Compute the rms value of the carrier voltage when i
has been armplitude modulated by asinusoidal audio voltage to a depth of (a) 30% (b; 50%.
[Ans. 81.78 volts;84.85 volts]
3.8. Unmodulated RF carrier power of 2 kW sends a current of 5 amp rms through an antenna.- On amplitude
moduiation by another sinusoidal voltage, the antenna curent increases to 5.9 amp. Calculate (a) the
modulation index and (b) carrier power after modulation.
[Ans. 80.3%;84.85 volts
3.9. The rms value of an RF voltage after arnplitude modulation to a depth of 30% by a sinusoida! modulating
voltage is 60 volts. Compute the rms value of the carrier voltage when amplitude modulated to depth of
70%.
[Ans. 65.49 volts
3.10. A broadcast transmitter radiates 1.08 kW when the modulation depth is 40 per cent. Calculate the total
power when the modulation index has been raised to 70 per cent.
[Ams. 1.245 kW
3.11. A radio transrnitter radiates 8 kW with the carrier unmoduiated and 8.64 kW when the carrier is modulated
by sinusoidal voltage of frequency f, Hz. Calculate the rnodulation index. Another sine wave of frequency
f is capabie of producing 50% modulation. If both the sine waves. simulaneously modulate the carier
determine the total radiated power.
(Ans. 9.64 k)
3.12. In an FM system, the frequency deviation is 4 kHz, when the audio modulating frequency is 200 Hz and the
audio modulating voltage is 4V. Compute the modulatior index. Also compute the frequency deviation and
modulation index if () AF. voltage is increased to 8V and modulation frequency is increased to 800 Hz (
AF voltage is increased to 12V and modulation frequency is deçreased to 100Hz.
[Ans. 20; 10,120]
3.13. An FM wave is represented by the voltage equation: p= 16 sin (4 x 1o't+6,sin 2000 ). Find the carriar
and the modulating frequencies, the modulation index and the maximurm frequency deviation of the FM.
What power will the FM voltage dissipate in a 12 ohm resistor ?
(Ans. f= 6.37 x10° Hz; fo=318 Hz:P= 10.66 watts

OBJECTIVE TYPE QUESTIONS

Pick up the correct choice.:

3.1. A sinusoidal voltage of amplitude 1 kV is amplitude modulated by another sinusoidal voltage to produe
30% modulation. The amplitude of each'sideband term is :(a) 300 volts (b) 150 volts (c) 500 volts () 100
volts.
A sinusoidal voltage amplitude modulates another sinusoidal voltage of amplitude 1 kV to result in two
3.2. sideband terms of arnplitude 200 volts each. The modulation index is (a) 0.5 (b) 0.4 (c) 0.2 () 0.1.
3.3. Acarrier voltage of unmodulated carrier power 1kW on being amplitude modulated by an audio sinusoidal
voltage to a depth of 100% has total modulated carrier power of: (a) 1.25 kW (b) 1.5 kW (c) 1.75 kW (0)2
kW.
TYPES OF MODULATION 59

3.4. In frequency modulation, the. modulation inoex is proportional to (a) o, (6) (c) o () where , is the
modulation frequency.
3.5. In FM broadcast, the maximum modulation frequency is : (a) 5 kHz (b) 10 kHz (c) 15 kHz () 25 kHz.
3.6. Infrequency modulation, the significant sidebands converge with increase of frequency : (a) True (b)
False.
8.7. In phase modulation, the significant sideband coverage with incroase of frequenoy :(a) True (6) False.
3.8. In FM,if the amplitude of the modulating voltage is doubled, the maximum frequency deviation: (a) doubles,
(b) becomes four times (c) becomes half (o) remains unaltered.
3.9. In FM, if the frequency of the modulating voltage is doubled, the rate of deviation of caries frequency :(a)
doubles (b,) becomes four times (c) becomes half (o) remains unaltered.
3.10. In FM, if the frequency of the modulating voltage is doubled, the maximum frequency deviation (a) doubles,
(b) becomes four times (c) becomes halt (d) remains unaltered.
3.11. In FM, if the' amplitude of the modulating voltage is doubled, the rate of deviation of carrier frequency : (a)
doubles, (b) becomes four times (c) becomes half (o) remains unaltered.
3.12. Sine wave of frequency fm modulates carrier of frequency f producing the same frequency deviation and
the same mdulation index in both FM and PM. Next if the modulation requency is doubled, the modulation
index in FM relative to that in PM willbe:(a) the same(b) halved (c) doubled (d) quadrupled.
ANSWERS

3.1. (b) 3.2. (b) 3.3. (b) 3.4. (6)

3.5. (c) 3.6. (a) 3.7. (b) 3.8. (a)
3.9. (a) 3.10. (c) 3.11 () 3.12 (b)